1. Technical Field
The present invention relates generally to the field of computer-implemented apparatus for numerical modelling, and more particularly to computer apparatus and computer-implemented method for numerical modelling of financial assets.
2. Description of Related Art
It is known to provide computer-implemented financial modelling tools that attempt to model or predict possible outcomes in relation to various financial assets. These tools are relatively complex, and are typically implemented using computer apparatus with sufficient memory, processing power, etc to perform the necessary calculations underlying the relevant model.
There is a long-standing economic theory of equilibrium as the equality of supply and demand in an exchange economy. This equilibrium theory has been developed since the first general formulation by Walras in 1874.
In the related art, some asset pricing models based upon cashflows have been developed outside of an equilibrium framework, for instance by Williams. Later methods like the Capital Asset Pricing Model (CAPM) of Sharpe, Lintner and Mossin are based upon the Mean-Variance Portfolio Construction Approach of Markowitz and the Tobin Separation Theorem.
The Mean-Variance approach uses a set of expected returns (the Mean part) and a variance-covariance matrix (the Variance part). This Mean-Variance approach presupposes that a probability distribution for returns is available and only the first two moments of the distribution are employed, so that higher order moments, like skew and kurtosis, are neglected. Thus the statistical basis of the Mean-Variance and its limitations have been pointed out by many parties since it was developed.
The CAPM was built with the Mean-Variance framework as its description of risk. The CAPM often described as an equilibrium theory because if all market participants share the same views on expected return and expected covariance of return then they will all hold the same portfolio, suitably levered to allow for their risk tolerance, and market clearing requires this to be the market cap weighted portfolio if markets are efficient.
The CAPM identifies the Market Portfolio as the efficient portfolio. The CAPM lead directly to the development of Market Capitalization investment products and indices that have grown to become the defacto benchmark in many markets, in particular developed equity markets. That is, it is known to provide computer-implemented financial models that output indices representing relative performance of a portfolio of financial assets, or provide portfolio constructions that allow a portfolio of the financial assets to be bought or sold.
As further background information see:
Williams, John Burr. 1938. The Theory of Investment Value, Harvard University Press, Cambridge Mass.
Lintner, John. 1965. The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. Review of Economics and Statistics. 47:1, pp. 13-37.
Markowitz, Harry. 1952. Portfolio Selection. Journal of Finance. 7:1, pp. 77-91.
Markowitz, Harry. 1959. Portfolio Selection: Efficient Diversification of Investments. Cowles Foundation Monograph No. 16. New York: John Wiley & Sons, Inc.
Markowitz, Harry. 2008. CAPM Investors Do Not Get Paid for Bearing Risk: A Linear Relation Does Not Imply Payment for Risk. Journal of Portfolio Management. 34:2 (Winter), pp. 91-94
Mossin, January 1966, Equilibrium in a Capital Asset Market, Econometrica, 34, pp. 768-783.
Roll, Richard. 1977. A Critique of the Asset Pricing Theory's Tests. Journal of Financial Economics, 4:2, pp. 129-176.
Sharpe, William F. 1964. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance. 19:3, pp. 425-442.
Tobin, James. 1958. Liquidity Preference as Behavior Toward Risk. Review of Economic Studies. 67, pp. 65-86.
Choueifaty, Yves and Yves Coignard, 2008. Toward Maximum Diversification, Journal of Portfolio Management. Fall 2008, 35:1, pp. 40-51.
A problem arises in that the market capitalization weighted proxies to the market portfolio have been demonstrated ex-post to be less efficient than a number of other methods of portfolio construction over long periods. Other criticisms have been made of the assumptions of the CAPM and ability to empirically prove the CAPM, such as in Roll. This has lead to a number of other approaches being developed to attempt to provide more efficient portfolios than the market capitalization weighted portfolios. These have included fundamental indexation by Arnott in U.S. Pat. No. 7,620,577, non-constant functions of capitalization weights by Fernholz in U.S. Pat. No. 5,819,238, and diversification based constructions by Choueifaty in US2008/222,252A1, and other more generic equally weighted and minimum variance portfolios.
It is now desired to provide an apparatus and method to implement a financial modelling tool. In particular, an apparatus and method are desired which output more detailed and/or more accurate financial modelling information.